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Maybe I missed something, but it seemed to me like “The Day of the Doctor” suggested that Hurt was the previously unknown 10th doctor, which would make Capaldi the 13th rather than the 12th.

I’m still confused about it.

http://www.patheos.com/blogs/exploringourmatrix/ James F. McGrath

Yes, it is all pretty confusing. He should be 9 if he is counted as a Doctor – following the eighth played by Paul McGann. Capaldi being the 13th would require counting the regeneration without changing his appearance during the David Tennant era, when he redirected the energy elsewhere.